Problem: Ricardo throws a stone off a bridge into a river below. The stone's height (in meters above the water), $x$ seconds after Ricardo threw it, is modeled by $w(x)=-5(x-8)(x+4)$ How many seconds after being thrown will the stone reach its maximum height?
Solution: The stone's height is modeled by a quadratic function, whose graph is a parabola. The maximum height is reached at the vertex. So in order to find when that happens, we need to find the vertex's $x$ -coordinate. The vertex's $x$ -coordinate is the average of the two zeros, so let's find those first. $\begin{aligned} w(x)&=0 \\\\ -5(x-8)(x+4)&=0 \\\\ \swarrow &\searrow \\\\ x-8=0\text{ or }&x+4=0 \\\\ x={8}\text{ or }&x={-4} \end{aligned}$ Now let's take the zeros' average: $\dfrac{({8})+({-4})}{2}=\dfrac42=2$ In conclusion, the stone will reach its maximum height after $2$ seconds.